Properties

Label 2001.1.bf.b.965.1
Level $2001$
Weight $1$
Character 2001.965
Analytic conductor $0.999$
Analytic rank $0$
Dimension $12$
Projective image $D_{28}$
CM discriminant -23
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2001.bf (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998629090279\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{28})\)
Defining polynomial: \(x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{28}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{28} - \cdots)\)

Embedding invariants

Embedding label 965.1
Root \(0.974928 + 0.222521i\) of defining polynomial
Character \(\chi\) \(=\) 2001.965
Dual form 2001.1.bf.b.620.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.623490 + 1.78183i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(-2.00435 - 1.59842i) q^{4} +(1.87590 + 0.211363i) q^{6} +(2.49939 - 1.57047i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\) \(q+(-0.623490 + 1.78183i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(-2.00435 - 1.59842i) q^{4} +(1.87590 + 0.211363i) q^{6} +(2.49939 - 1.57047i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(-1.11233 + 2.30978i) q^{12} +(-1.75676 + 0.400969i) q^{13} +(0.669500 + 2.93327i) q^{16} +(-0.211363 - 1.87590i) q^{18} +(-0.433884 + 0.900969i) q^{23} +(-2.08726 - 2.08726i) q^{24} +(0.623490 - 0.781831i) q^{25} +(0.380863 - 3.38025i) q^{26} +(0.623490 + 0.781831i) q^{27} +(0.781831 + 0.623490i) q^{29} +(1.33485 + 0.467085i) q^{31} +(-2.71075 - 0.305428i) q^{32} +(2.49939 + 0.570469i) q^{36} +(0.781831 + 1.62349i) q^{39} +(0.752407 + 0.752407i) q^{41} +(-1.33485 - 1.33485i) q^{46} +(-1.05737 + 1.68280i) q^{47} +(2.71075 - 1.30543i) q^{48} +(-0.222521 + 0.974928i) q^{49} +(1.00435 + 1.59842i) q^{50} +(4.16208 + 2.00435i) q^{52} +(-1.78183 + 0.623490i) q^{54} +(-1.59842 + 1.00435i) q^{58} +1.24698i q^{59} +(-1.66453 + 2.08726i) q^{62} +(0.928918 - 1.92892i) q^{64} +(0.974928 + 0.222521i) q^{69} +(-0.193096 - 0.846011i) q^{71} +(-1.57047 + 2.49939i) q^{72} +(1.87590 - 0.656405i) q^{73} +(-0.900969 - 0.433884i) q^{75} +(-3.38025 + 0.380863i) q^{78} +(0.623490 - 0.781831i) q^{81} +(-1.80978 + 0.871544i) q^{82} +(0.433884 - 0.900969i) q^{87} +(2.30978 - 1.11233i) q^{92} +(0.158342 - 1.40532i) q^{93} +(-2.33921 - 2.93327i) q^{94} +(0.305428 + 2.71075i) q^{96} +(-1.59842 - 1.00435i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} - 2q^{3} - 14q^{4} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 12q + 2q^{2} - 2q^{3} - 14q^{4} + 2q^{6} - 2q^{9} + 12q^{16} + 2q^{18} - 2q^{25} + 4q^{26} - 2q^{27} + 2q^{31} + 2q^{32} - 2q^{41} - 2q^{46} + 2q^{47} - 2q^{48} - 2q^{49} + 2q^{50} + 10q^{52} - 12q^{54} + 2q^{58} - 4q^{62} - 14q^{64} - 14q^{72} + 2q^{73} - 2q^{75} - 10q^{78} - 2q^{81} + 4q^{82} + 2q^{92} + 2q^{93} - 4q^{94} - 12q^{96} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2001\mathbb{Z}\right)^\times\).

\(n\) \(553\) \(668\) \(1132\)
\(\chi(n)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.623490 + 1.78183i −0.623490 + 1.78183i 1.00000i \(0.5\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(3\) −0.222521 0.974928i −0.222521 0.974928i
\(4\) −2.00435 1.59842i −2.00435 1.59842i
\(5\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(6\) 1.87590 + 0.211363i 1.87590 + 0.211363i
\(7\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(8\) 2.49939 1.57047i 2.49939 1.57047i
\(9\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(10\) 0 0
\(11\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(12\) −1.11233 + 2.30978i −1.11233 + 2.30978i
\(13\) −1.75676 + 0.400969i −1.75676 + 0.400969i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.669500 + 2.93327i 0.669500 + 2.93327i
\(17\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(18\) −0.211363 1.87590i −0.211363 1.87590i
\(19\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(24\) −2.08726 2.08726i −2.08726 2.08726i
\(25\) 0.623490 0.781831i 0.623490 0.781831i
\(26\) 0.380863 3.38025i 0.380863 3.38025i
\(27\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(28\) 0 0
\(29\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(30\) 0 0
\(31\) 1.33485 + 0.467085i 1.33485 + 0.467085i 0.900969 0.433884i \(-0.142857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(32\) −2.71075 0.305428i −2.71075 0.305428i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 2.49939 + 0.570469i 2.49939 + 0.570469i
\(37\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(38\) 0 0
\(39\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(40\) 0 0
\(41\) 0.752407 + 0.752407i 0.752407 + 0.752407i 0.974928 0.222521i \(-0.0714286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(42\) 0 0
\(43\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −1.33485 1.33485i −1.33485 1.33485i
\(47\) −1.05737 + 1.68280i −1.05737 + 1.68280i −0.433884 + 0.900969i \(0.642857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(48\) 2.71075 1.30543i 2.71075 1.30543i
\(49\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(50\) 1.00435 + 1.59842i 1.00435 + 1.59842i
\(51\) 0 0
\(52\) 4.16208 + 2.00435i 4.16208 + 2.00435i
\(53\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(54\) −1.78183 + 0.623490i −1.78183 + 0.623490i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −1.59842 + 1.00435i −1.59842 + 1.00435i
\(59\) 1.24698i 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(60\) 0 0
\(61\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(62\) −1.66453 + 2.08726i −1.66453 + 2.08726i
\(63\) 0 0
\(64\) 0.928918 1.92892i 0.928918 1.92892i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(68\) 0 0
\(69\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(70\) 0 0
\(71\) −0.193096 0.846011i −0.193096 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(72\) −1.57047 + 2.49939i −1.57047 + 2.49939i
\(73\) 1.87590 0.656405i 1.87590 0.656405i 0.900969 0.433884i \(-0.142857\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(74\) 0 0
\(75\) −0.900969 0.433884i −0.900969 0.433884i
\(76\) 0 0
\(77\) 0 0
\(78\) −3.38025 + 0.380863i −3.38025 + 0.380863i
\(79\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(80\) 0 0
\(81\) 0.623490 0.781831i 0.623490 0.781831i
\(82\) −1.80978 + 0.871544i −1.80978 + 0.871544i
\(83\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.433884 0.900969i 0.433884 0.900969i
\(88\) 0 0
\(89\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.30978 1.11233i 2.30978 1.11233i
\(93\) 0.158342 1.40532i 0.158342 1.40532i
\(94\) −2.33921 2.93327i −2.33921 2.93327i
\(95\) 0 0
\(96\) 0.305428 + 2.71075i 0.305428 + 2.71075i
\(97\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(98\) −1.59842 1.00435i −1.59842 1.00435i
\(99\) 0 0
\(100\) −2.49939 + 0.570469i −2.49939 + 0.570469i
\(101\) −1.87590 + 0.656405i −1.87590 + 0.656405i −0.900969 + 0.433884i \(0.857143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(102\) 0 0
\(103\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(104\) −3.76111 + 3.76111i −3.76111 + 3.76111i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(108\) 2.56366i 2.56366i
\(109\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.570469 2.49939i −0.570469 2.49939i
\(117\) 1.40881 1.12349i 1.40881 1.12349i
\(118\) −2.22191 0.777479i −2.22191 0.777479i
\(119\) 0 0
\(120\) 0 0
\(121\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(122\) 0 0
\(123\) 0.566116 0.900969i 0.566116 0.900969i
\(124\) −1.92892 3.06986i −1.92892 3.06986i
\(125\) 0 0
\(126\) 0 0
\(127\) −0.566116 + 0.900969i −0.566116 + 0.900969i 0.433884 + 0.900969i \(0.357143\pi\)
−1.00000 \(\pi\)
\(128\) 0.928918 + 0.928918i 0.928918 + 0.928918i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.218169 + 0.623490i 0.218169 + 0.623490i 1.00000 \(0\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(138\) −1.00435 + 1.59842i −1.00435 + 1.59842i
\(139\) 0.781831 + 0.376510i 0.781831 + 0.376510i 0.781831 0.623490i \(-0.214286\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 1.87590 + 0.656405i 1.87590 + 0.656405i
\(142\) 1.62784 + 0.183414i 1.62784 + 0.183414i
\(143\) 0 0
\(144\) −1.87590 2.35230i −1.87590 2.35230i
\(145\) 0 0
\(146\) 3.75179i 3.75179i
\(147\) 1.00000 1.00000
\(148\) 0 0
\(149\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(150\) 1.33485 1.33485i 1.33485 1.33485i
\(151\) −0.867767 + 1.80194i −0.867767 + 1.80194i −0.433884 + 0.900969i \(0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.02795 4.50374i 1.02795 4.50374i
\(157\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00435 + 1.59842i 1.00435 + 1.59842i
\(163\) −1.68280 1.05737i −1.68280 1.05737i −0.900969 0.433884i \(-0.857143\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(164\) −0.305428 2.71075i −0.305428 2.71075i
\(165\) 0 0
\(166\) 0 0
\(167\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(168\) 0 0
\(169\) 2.02446 0.974928i 2.02446 0.974928i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.445042 0.445042 0.222521 0.974928i \(-0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(174\) 1.33485 + 1.33485i 1.33485 + 1.33485i
\(175\) 0 0
\(176\) 0 0
\(177\) 1.21572 0.277479i 1.21572 0.277479i
\(178\) 0 0
\(179\) −0.400969 + 0.193096i −0.400969 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(180\) 0 0
\(181\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.330500 + 2.93327i 0.330500 + 2.93327i
\(185\) 0 0
\(186\) 2.40532 + 1.15834i 2.40532 + 1.15834i
\(187\) 0 0
\(188\) 4.80917 1.68280i 4.80917 1.68280i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −2.08726 0.476403i −2.08726 0.476403i
\(193\) 0.222521 0.0250721i 0.222521 0.0250721i 1.00000i \(-0.5\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 2.00435 1.59842i 2.00435 1.59842i
\(197\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(198\) 0 0
\(199\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(200\) 0.330500 2.93327i 0.330500 2.93327i
\(201\) 0 0
\(202\) 3.75179i 3.75179i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000i 1.00000i
\(208\) −2.35230 4.88460i −2.35230 4.88460i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.752407 1.19745i −0.752407 1.19745i −0.974928 0.222521i \(-0.928571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(212\) 0 0
\(213\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(214\) 0 0
\(215\) 0 0
\(216\) 2.78618 + 0.974928i 2.78618 + 0.974928i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.05737 1.68280i −1.05737 1.68280i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(226\) 0 0
\(227\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(228\) 0 0
\(229\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.93327 + 0.330500i 2.93327 + 0.330500i
\(233\) 0.445042i 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(234\) 1.12349 + 3.21075i 1.12349 + 3.21075i
\(235\) 0 0
\(236\) 1.99319 2.49939i 1.99319 2.49939i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.52446 1.21572i 1.52446 1.21572i 0.623490 0.781831i \(-0.285714\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(240\) 0 0
\(241\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(242\) −1.87590 + 0.211363i −1.87590 + 0.211363i
\(243\) −0.900969 0.433884i −0.900969 0.433884i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.25241 + 1.57047i 1.25241 + 1.57047i
\(247\) 0 0
\(248\) 4.06986 0.928918i 4.06986 0.928918i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1.25241 1.57047i −1.25241 1.57047i
\(255\) 0 0
\(256\) −0.305428 + 0.147086i −0.305428 + 0.147086i
\(257\) 1.22252 + 0.974928i 1.22252 + 0.974928i 1.00000 \(0\)
0.222521 + 0.974928i \(0.428571\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −0.974928 0.222521i −0.974928 0.222521i
\(262\) −1.24698 −1.24698
\(263\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.900969 0.566116i 0.900969 0.566116i 1.00000i \(-0.5\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(270\) 0 0
\(271\) 0.0739590 + 0.656405i 0.0739590 + 0.656405i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.59842 2.00435i −1.59842 2.00435i
\(277\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(278\) −1.15834 + 1.15834i −1.15834 + 1.15834i
\(279\) −1.40532 + 0.158342i −1.40532 + 0.158342i
\(280\) 0 0
\(281\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(282\) −2.33921 + 2.93327i −2.33921 + 2.93327i
\(283\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(284\) −0.965245 + 2.00435i −0.965245 + 2.00435i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.57482 0.900969i 2.57482 0.900969i
\(289\) 1.00000i 1.00000i
\(290\) 0 0
\(291\) 0 0
\(292\) −4.80917 1.68280i −4.80917 1.68280i
\(293\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(294\) −0.623490 + 1.78183i −0.623490 + 1.78183i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.400969 1.75676i 0.400969 1.75676i
\(300\) 1.11233 + 2.30978i 1.11233 + 2.30978i
\(301\) 0 0
\(302\) −2.66971 2.66971i −2.66971 2.66971i
\(303\) 1.05737 + 1.68280i 1.05737 + 1.68280i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.158342 + 0.158342i 0.158342 + 0.158342i 0.781831 0.623490i \(-0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.00435 1.59842i −1.00435 1.59842i −0.781831 0.623490i \(-0.785714\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(312\) 4.50374 + 2.82989i 4.50374 + 2.82989i
\(313\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.78183 0.623490i −1.78183 0.623490i −0.781831 0.623490i \(-0.785714\pi\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −2.49939 + 0.570469i −2.49939 + 0.570469i
\(325\) −0.781831 + 1.62349i −0.781831 + 1.62349i
\(326\) 2.93327 2.33921i 2.93327 2.33921i
\(327\) 0 0
\(328\) 3.06219 + 0.698924i 3.06219 + 0.698924i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.19745 + 1.19745i −1.19745 + 1.19745i −0.222521 + 0.974928i \(0.571429\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 3.21075 1.12349i 3.21075 1.12349i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(338\) 0.474928 + 4.21510i 0.474928 + 4.21510i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.277479 + 0.792990i −0.277479 + 0.792990i
\(347\) 1.94986 1.94986 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(348\) −2.30978 + 1.11233i −2.30978 + 1.11233i
\(349\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(350\) 0 0
\(351\) −1.40881 1.12349i −1.40881 1.12349i
\(352\) 0 0
\(353\) −1.75676 + 0.846011i −1.75676 + 0.846011i −0.781831 + 0.623490i \(0.785714\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(354\) −0.263565 + 2.33921i −0.263565 + 2.33921i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.0940653 0.834853i −0.0940653 0.834853i
\(359\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(360\) 0 0
\(361\) 0.974928 0.222521i 0.974928 0.222521i
\(362\) 0 0
\(363\) 0.781831 0.623490i 0.781831 0.623490i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(368\) −2.93327 0.669500i −2.93327 0.669500i
\(369\) −1.00435 0.351438i −1.00435 0.351438i
\(370\) 0 0
\(371\) 0 0
\(372\) −2.56366 + 2.56366i −2.56366 + 2.56366i
\(373\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 5.86654i 5.86654i
\(377\) −1.62349 0.781831i −1.62349 0.781831i
\(378\) 0 0
\(379\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(380\) 0 0
\(381\) 1.00435 + 0.351438i 1.00435 + 0.351438i
\(382\) 0 0
\(383\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(384\) 0.698924 1.11233i 0.698924 1.11233i
\(385\) 0 0
\(386\) −0.0940653 + 0.412127i −0.0940653 + 0.412127i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.974928 + 2.78618i 0.974928 + 2.78618i
\(393\) 0.559311 0.351438i 0.559311 0.351438i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.433884 1.90097i 0.433884 1.90097i 1.00000i \(-0.5\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 2.71075 + 1.30543i 2.71075 + 1.30543i
\(401\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(402\) 0 0
\(403\) −2.53230 0.285322i −2.53230 0.285322i
\(404\) 4.80917 + 1.68280i 4.80917 + 1.68280i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.119137 + 1.05737i −0.119137 + 1.05737i 0.781831 + 0.623490i \(0.214286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 1.78183 + 0.623490i 1.78183 + 0.623490i
\(415\) 0 0
\(416\) 4.88460 0.550362i 4.88460 0.550362i
\(417\) 0.193096 0.846011i 0.193096 0.846011i
\(418\) 0 0
\(419\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(420\) 0 0
\(421\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(422\) 2.60277 0.594065i 2.60277 0.594065i
\(423\) 0.222521 1.97493i 0.222521 1.97493i
\(424\) 0 0
\(425\) 0 0
\(426\) −0.183414 1.62784i −0.183414 1.62784i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(432\) −1.87590 + 2.35230i −1.87590 + 2.35230i
\(433\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 3.65773 0.834853i 3.65773 0.834853i
\(439\) 1.52446 + 1.21572i 1.52446 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(440\) 0 0
\(441\) −0.222521 0.974928i −0.222521 0.974928i
\(442\) 0 0
\(443\) 0.189606 0.119137i 0.189606 0.119137i −0.433884 0.900969i \(-0.642857\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.711363 0.446979i −0.711363 0.446979i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.623490 0.218169i 0.623490 0.218169i 1.00000i \(-0.5\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(450\) −1.59842 1.00435i −1.59842 1.00435i
\(451\) 0 0
\(452\) 0 0
\(453\) 1.94986 + 0.445042i 1.94986 + 0.445042i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.189606 + 1.68280i −0.189606 + 1.68280i 0.433884 + 0.900969i \(0.357143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(462\) 0 0
\(463\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(464\) −1.30543 + 2.71075i −1.30543 + 2.71075i
\(465\) 0 0
\(466\) −0.792990 0.277479i −0.792990 0.277479i
\(467\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(468\) −4.61956 −4.61956
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 1.95834 + 3.11668i 1.95834 + 3.11668i
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 1.21572 + 3.47431i 1.21572 + 3.47431i
\(479\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.570469 2.49939i 0.570469 2.49939i
\(485\) 0 0
\(486\) 1.33485 1.33485i 1.33485 1.33485i
\(487\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(488\) 0 0
\(489\) −0.656405 + 1.87590i −0.656405 + 1.87590i
\(490\) 0 0
\(491\) −1.59842 0.559311i −1.59842 0.559311i −0.623490 0.781831i \(-0.714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(492\) −2.57482 + 0.900969i −2.57482 + 0.900969i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.476403 + 4.22820i −0.476403 + 4.22820i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.541044 1.12349i 0.541044 1.12349i −0.433884 0.900969i \(-0.642857\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(500\) 0 0
\(501\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(502\) 0 0
\(503\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.40097 1.75676i −1.40097 1.75676i
\(508\) 2.57482 0.900969i 2.57482 0.900969i
\(509\) 1.52446 0.347948i 1.52446 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.0754345 + 0.669500i 0.0754345 + 0.669500i
\(513\) 0 0
\(514\) −2.49939 + 1.57047i −2.49939 + 1.57047i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.0990311 0.433884i −0.0990311 0.433884i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 1.00435 1.59842i 1.00435 1.59842i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0.559311 1.59842i 0.559311 1.59842i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.623490 0.781831i −0.623490 0.781831i
\(530\) 0 0
\(531\) −0.541044 1.12349i −0.541044 1.12349i
\(532\) 0 0
\(533\) −1.62349 1.02011i −1.62349 1.02011i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(538\) 0.446979 + 1.95834i 0.446979 + 1.95834i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.222521 0.0250721i 0.222521 0.0250721i 1.00000i \(-0.5\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(542\) −1.21572 0.277479i −1.21572 0.277479i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 2.78618 0.974928i 2.78618 0.974928i
\(553\) 0 0
\(554\) −3.38025 0.380863i −3.38025 0.380863i
\(555\) 0 0
\(556\) −0.965245 2.00435i −0.965245 2.00435i
\(557\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(558\) 0.594065 2.60277i 0.594065 2.60277i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) −2.71075 4.31413i −2.71075 4.31413i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −1.81126 1.81126i −1.81126 1.81126i
\(569\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(570\) 0 0
\(571\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(576\) 2.14094i 2.14094i
\(577\) 1.68280 + 0.189606i 1.68280 + 0.189606i 0.900969 0.433884i \(-0.142857\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(578\) 1.78183 + 0.623490i 1.78183 + 0.623490i
\(579\) −0.0739590 0.211363i −0.0739590 0.211363i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 3.65773 4.58665i 3.65773 4.58665i
\(585\) 0 0
\(586\) 0 0
\(587\) −1.52446 + 1.21572i −1.52446 + 1.21572i −0.623490 + 0.781831i \(0.714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(588\) −2.00435 1.59842i −2.00435 1.59842i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.433884 + 1.90097i 0.433884 + 1.90097i 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 2.88025 + 1.80978i 2.88025 + 1.80978i
\(599\) −0.0739590 0.656405i −0.0739590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(600\) −2.93327 + 0.330500i −2.93327 + 0.330500i
\(601\) 1.19745 0.752407i 1.19745 0.752407i 0.222521 0.974928i \(-0.428571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.61956 2.22466i 4.61956 2.22466i
\(605\) 0 0
\(606\) −3.65773 + 0.834853i −3.65773 + 0.834853i
\(607\) −0.559311 + 1.59842i −0.559311 + 1.59842i 0.222521 + 0.974928i \(0.428571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.18280 3.38025i 1.18280 3.38025i
\(612\) 0 0
\(613\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(614\) −0.380863 + 0.183414i −0.380863 + 0.183414i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(618\) 0 0
\(619\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(620\) 0 0
\(621\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(622\) 3.47431 0.792990i 3.47431 0.792990i
\(623\) 0 0
\(624\) −4.23870 + 3.38025i −4.23870 + 3.38025i
\(625\) −0.222521 0.974928i −0.222521 0.974928i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(632\) 0 0
\(633\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(634\) 2.22191 2.78618i 2.22191 2.78618i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.80194i 1.80194i
\(638\) 0 0
\(639\) 0.541044 + 0.678448i 0.541044 + 0.678448i
\(640\) 0 0
\(641\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(642\) 0 0
\(643\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.347948 + 1.52446i −0.347948 + 1.52446i 0.433884 + 0.900969i \(0.357143\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(648\) 0.330500 2.93327i 0.330500 2.93327i
\(649\) 0 0
\(650\) −2.40532 2.40532i −2.40532 2.40532i
\(651\) 0 0
\(652\) 1.68280 + 4.80917i 1.68280 + 4.80917i
\(653\) −0.467085 1.33485i −0.467085 1.33485i −0.900969 0.433884i \(-0.857143\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.70328 + 2.71075i −1.70328 + 2.71075i
\(657\) −1.40532 + 1.40532i −1.40532 + 1.40532i
\(658\) 0 0
\(659\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(660\) 0 0
\(661\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(662\) −1.38705 2.88025i −1.38705 2.88025i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(668\) 4.61956i 4.61956i
\(669\) 0.445042 0.445042
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.846011 1.75676i 0.846011 1.75676i 0.222521 0.974928i \(-0.428571\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(674\) 0 0
\(675\) 1.00000 1.00000
\(676\) −5.61607 1.28183i −5.61607 1.28183i
\(677\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.52446 + 0.347948i −1.52446 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(0.5\pi\)
\(692\) −0.892021 0.711363i −0.892021 0.711363i
\(693\) 0 0
\(694\) −1.21572 + 3.47431i −1.21572 + 3.47431i
\(695\) 0 0
\(696\) −0.330500 2.93327i −0.330500 2.93327i
\(697\) 0 0
\(698\) −0.777479 + 2.22191i −0.777479 + 2.22191i
\(699\) 0.433884 0.0990311i 0.433884 0.0990311i
\(700\) 0 0
\(701\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(702\) 2.88025 1.80978i 2.88025 1.80978i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.412127 3.65773i −0.412127 3.65773i
\(707\) 0 0
\(708\) −2.88025 1.38705i −2.88025 1.38705i
\(709\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.00000 + 1.00000i −1.00000 + 1.00000i
\(714\) 0 0
\(715\) 0 0
\(716\) 1.11233 + 0.253882i 1.11233 + 0.253882i
\(717\) −1.52446 1.21572i −1.52446 1.21572i
\(718\) 0 0
\(719\) 0.376510 0.781831i 0.376510 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
1.00000 \(0\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.211363 + 1.87590i −0.211363 + 1.87590i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.974928 0.222521i 0.974928 0.222521i
\(726\) 0.623490 + 1.78183i 0.623490 + 1.78183i
\(727\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(728\) 0 0
\(729\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 1.45133 2.30978i 1.45133 2.30978i
\(737\) 0 0
\(738\) 1.25241 1.57047i 1.25241 1.57047i
\(739\) 0.351438 + 1.00435i 0.351438 + 1.00435i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(744\) −1.81126 3.76111i −1.81126 3.76111i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(752\) −5.64402 1.97493i −5.64402 1.97493i
\(753\) 0 0
\(754\) 2.40532 2.40532i 2.40532 2.40532i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.40881 + 1.12349i −1.40881 + 1.12349i −0.433884 + 0.900969i \(0.642857\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(762\) −1.25241 + 1.57047i −1.25241 + 1.57047i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.500000 2.19064i −0.500000 2.19064i
\(768\) 0.211363 + 0.265041i 0.211363 + 0.265041i
\(769\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(770\) 0 0
\(771\) 0.678448 1.40881i 0.678448 1.40881i
\(772\) −0.486086 0.305428i −0.486086 0.305428i
\(773\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(774\) 0 0
\(775\) 1.19745 0.752407i 1.19745 0.752407i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 1.00000i 1.00000i
\(784\) −3.00870 −3.00870
\(785\) 0 0
\(786\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(787\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 3.11668 + 1.95834i 3.11668 + 1.95834i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(798\) 0 0